Grades 9-10 Video Solutions 2025-2025_9-10

Video Transcription

Video Summary

The problem explores a 4-digit integer \((a, b, c, d)\) multiplied by its unit digit \(d\) to form another integer where the units and thousands digit switch places. By analyzing the conditions, \(a\) was determined to be 1 since \(a\) cannot be 0. For \(d\), the only valid digit satisfying the condition of \(d^2\) ending with \(a\) is 9. Consequently, \(a, b, c, d\) becomes \(1, b, c, 9\) and must be less than or equal to 1111. Thus, \(b\) and \(c\) can range from 00 to 10, yielding 11 possible combinations satisfying the problem's conditions.

Keywords

4-digit integer

unit digit

digit switch

valid digit

combinations